Theorems · Theorem · order theory
refl
∀ {α : Sort u_1} {r : α → α → Prop} [Std.Refl r] (a : α), r a a- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 80 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- Std.Refl
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by80
Results whose statement or proof uses this declaration.
- IsChain.directedOnproof · cited by 28
- IsChain.totalproof · cited by 12
- AlgebraicGeometry.Scheme.isoOfEq_rflstatement and proof · cited by 12
- refl_ofproof · cited by 9
- Relation.EqvGen.eqvGen_leproof · cited by 6
- AlgebraicGeometry.Scheme.homOfLE_rflstatement and proof · cited by 6
- Polynomial.cyclotomic_eq_prod_X_sub_primitiveRootsproof · cited by 5
- Relation.reflTransGen_eq_selfproof · cited by 5
- IsChain.directedproof · cited by 4
- Nat.rel_of_forall_rel_succ_of_le_of_leproof · cited by 4
- Std.Total.directedOnproof · cited by 3
- of_eqproof · cited by 3